Question

Which equation is the inverse of f(x)=LaTeX: \frac{1}{x+2}1 x + 2 A. LaTeX: f^{-1}\left(x\right)=\frac{1}{x}+2f − 1 ( x ) = 1 x + 2 B. LaTeX: f^{-1}\left(x\right)=\frac{1}{x}-2f − 1 ( x ) = 1 x − 2 C. LaTeX: f^{-1}\left(x\right)=2-\frac{1}{x}f − 1 ( x ) = 2 − 1 x D. LaTeX: f^{-1}\left(x\right)=-2-\frac{1}{x}f − 1 ( x ) = − 2 − 1 x

Answer 1

Answer:

$g^{-1}x = \frac{1-2x}{x}$

Step-by-step explanation:

Given the function $g(x)= \frac{1}{x+2}$, we are to find the inverse of the function and this can be done y following the simple steps:

Step 1: Replace y with $g(x)$

$g(x)= \frac{1}{x+2}\\y= \frac{1}{x+2}$

Step 2: Interchange x with y

$x= \frac{1}{y+2}$

Step 3: Make y the subject of the formula;

$x= \frac{1}{y+2}\\y+2 = \frac{1}{x}\\y = \frac{1}{x} - 2\\Find \ the\ LCM\\y = \frac{1-2x}{x}$

Step 4: Replace y as $g^{-1}(x)$

$g^{-1}x = \frac{1-2x}{x}$

Hence the inverse of the function is $g^{-1}x = \frac{1-2x}{x}$